∫
1
2
1
x
2
d
x
=
\displaystyle \int \limits_1^2 \dfrac{1}{x^2} dx =
1
∫
2
x
2
1
d
x
=
−
1
2
-\dfrac{1}{2}
−
2
1
7
4
\dfrac{7}{4}
4
7
1
2
\dfrac{1}{2}
2
1
1
1
1
Summary
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Approach
Rewriting the integrand,
∫
1
2
1
x
2
d
x
=
∫
1
2
x
−
2
d
x
=
\int \limits_1^2 \dfrac{1}{x^2} dx = \int \limits_1^2 x^{-2} dx =
1
∫
2
x
2
1
d
x
=
1
∫
2
x
−
2
d
x
=
=
[
−
x
−
1
]
1
2
=
[
−
1
x
]
1
2
= \Big[ -x^{-1} \Big]_1^2 = \left[ -\frac{1}{x} \right]_1^2
=
[
−
x
−
1
]
1
2
=
[
−
x
1
]
1
2
=
−
(
1
2
−
1
1
)
= -\left( \frac{1}{2} - \frac{1}{1} \right)
=
−
(
2
1
−
1
1
)
=
1
2
= \frac{1}{2}
=
2
1